Visualization and Processing of Tensor Fields

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Weickert, Joachim (Επιμελητής έκδοσης), Hagen, Hans (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Mathematics and Visualization,
• Θέματα: Mathematics.; Radiology.; Computer graphics.; Image processing.; Mathematical analysis.; Analysis (Mathematics).; Visualization.; Differential geometry.; Analysis.; Imaging / Radiology.; Computer Imaging, Vision, Pattern Recognition and Graphics.; Image Processing and Computer Vision.; Differential Geometry.

 Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state-of-the-art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students. 

 An Introduction to Tensors -- Feature Detection with Tensors -- Adaptive Structure Tensors and their Applications -- On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor -- Low-level Feature Detection Using the Boundary Tensor -- Diffusion Tensor Imaging -- An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond -- Random Noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections -- An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications -- Anatomy-Based Visualizations of Diffusion Tensor Images of Brain White Matter -- Variational Regularization of Multiple Diffusion Tensor Fields -- Higher Rank Tensors in Diffusion MRI -- Visualization of Tensor Fields -- Strategies for Direct Visualization of Second-Rank Tensor Fields -- Tensor Invariants and their Gradients -- Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields -- Degenerate 3D Tensors -- Locating Closed Hyperstreamlines in Second Order Tensor Fields -- Tensor Field Visualization Using a Metric Interpretation -- Tensor Field Transformations -- Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization -- Continuous Tensor Field Approximation of Diffusion Tensor MRI data -- Tensor Field Interpolation with PDEs -- Diffusion-Tensor Image Registration -- Image Processing Methods for Tensor Fields -- Tensor Median Filtering and M-Smoothing -- Mathematical Morphology on Tensor Data Using the Loewner Ordering -- A Local Structure Measure for Anisotropic Regularization of Tensor Fields -- Tensor Field Regularization using Normalized Convolution and Markov Random Fields in a Bayesian Framework -- PDEs for Tensor Image Processing.